Measurement of nano particle adhesion by atomic force microscopy using probability theory based analysis

We present a method to detect adhesive forces of nano particles by analysis of the distribution of measured lateral forces. The measurement protocol is suitable for all types of atomic force microscopes with a lateral force channel. Lateral forces are measured, in constant normal force contact mode, by scanning of substrates decorated with nano beads. By using probability theory, geometry based measurement errors are compensated and the real adhesion force is determined within a given confidence interval. The theoretical model can be adapted for particles with arbitrary shape and distribution of adhesion forces. It is applied to the adhesion problem of spherical particles with a Gaussian distribution of adhesion forces. We analyze the measured force distribution qualitatively and quantitatively. The theory predicts a systematic underestimation of the mean value of any particle adhesion measurement done by lateral pushing. Real measurement data of 50 nm diameter silica nano beads on silicon substrate is used to test the theoretical model for plausibility by means of information theory.